"we and someone" vs "someone and we"

Both:

I and my neighbour went to the races

and:

My neighbour and I went to the races

are commonly used. However in the plural I've only ever seen the form:

We and the neighbours went to the races

The other form:

The neighbours and we went to the races

sounds drastically wrong for some reason I can't articulate, but I don't think it violates any grammatical rules. Is My neighbours and we incorrect in this context, or does it seem strange simply because it isn't commonly used?

It doesn't appear that any answer is forthcoming, so I'll post what I think is the consensus amongst the commenters as an answer.

There is nothing grammatically wrong with the construction:

The neighbours and we went to the races

but it's ugly, and in practice you would use an alternative form like We went to the races with the neighbours.

I cannot find any definitive statement on the subject. The nearest I found is on the blog written by Patricia T. O’Conner, who is the author of several grammar books. She addresses the question in this blog article and states that she believes it to be grammatically correct though she can't find a supporting authority either.